From Folding to Replication: Differentiable Filament--Field Models Across Biological Scales

Filaments organize biological systems across scales, from protein-like polymers to cytoskeletons, flagella and whole organisms. How organization at one scale enables function at the next is a question at the heart of the origins of life and of multicellularity, and it is hard to study when each system is simulated separately. Multiscale methods usually bridge scales by passing coarse-grained parameters between models or by stitching simulations of different resolution together; we instead reuse the same three physical ingredients at every scale: flexible chains, interactions transmitted through surrounding spatial fields, and bonds that can form or break. We report three results within this filament--field approach. First, local preferred curvature constructs a target fold during growth, but specific contacts between distant parts of the chain are needed to maintain it at finite temperature and recover it after denaturation. Second, uneven filament growth against a membrane and a swimming stroke that does not retrace itself both produce directed motion, showing the importance of broken symmetry. Third, local binding, templating and physical separation allow polymer strands to copy. Together, these results show how one physically grounded approach can connect sequence, structure, interaction and function across simplified biological scales, providing a cheap, measurable environment for testing multiscale hypotheses before committing laboratory or large-scale compute resources.